Cathy has 48m of fencing to make a rectangular pen for her pets. What is the
maximum area?

The average rate of change of the function f( x ) = x² + 7x + 6 at the interval of −4 ≤ x ≤ −1 is 2

The average rate of change the function is simply the change in y-values of the two points divided by the change in x-values of the two points.

It is expressed as;

Given the data in the question;

Average rate of change = ( f(-1) - f(-4) ) / ( (-1) - (-4) )

Average rate of change = ( (-1)² + 7(-1) + 6 ) - ( (-4)² + 7(-4) + 6 ) ) / ( (-1) - (-4) )

Average rate of change = ( (1 + -7 + 6 ) - ( 16 - 28 + 6 ) ) / (-1 + 4 )

Average rate of change = ( ( 0 ) - ( -6 ) ) / (-1 + 4 )

Average rate of change = ( 0 + 6 ) / ( 3 )

Average rate of change = 6 / 3

Average rate of change = 2

Therefore, the average rate of change of the function is 2.

Learn more about average rate of change here: https://brainly.com/question/28744270

#SPJ1

Using the Pythagorean Theorem, it is found that:

The Pythagorean Theorem is a geometry axion relates the length of the sides [tex]l_1[/tex] and [tex]l_2[/tex], which are the separated by the angle of 90º, of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

For the netting, it is found that:

Hence the measure c, representing the length of the bar, is calculated as follows:

c² = 8² + 3.5²

c = sqrt(8² + 3.5²)

c = 8.73 ft.

The amount of netting needed is the area of the entire goal, composed by:

Hence:

A = 12 x 8.73 + 2 x 1/2 x 8 x 3.5 = 132.76 ft².

More can be learned about the Pythagorean Theorem at https://brainly.com/question/343682

#SPJ1

If Milly knits a scarf that is 1.2 m long then Lotte's scarf be 2.20 in metres.

We will use unitary method to solve this problem.

We know, Milly and Lotte are knitting scarves.

For every 6 cm that Milly knits, Lotte knits 11 cm. This can also be written as,

6 cm Milly knits    ---------------->  11 cm  Lotte knits

1 cm Milly knits    ---------------->  (11/6 ) cm  Lotte knits

We know, 1m = 100cm. So, we can write

120 cm Milly knits    ---------------->  ( 11/6 ) × 120 cm  Lotte knits

120 cm Milly knits    ---------------->  220 cm  Lotte knits

120 cm Milly knits    ---------------->  2.20 m  Lotte knits

Thus, we can conclude that  if Milly knits a scarf that is 1.2 m long then  Lotte knits 2.20 metres scarf .

To know more about Unitary Method refer to the link:

https://brainly.com/question/23423168

#SPJ9

Answer:

answer is A

as the graph cuts the x axis at 4 which is shown by (x-4). and cut by -2 and -4 which is shown by (x+2) and (x+4).

1.242 ≤ d ≤ 1.305 is the corresponding interval for the diameter of the washer.

Given that,

Company A makes and sells a washer having a 4-centimeter outer radius. The corporation has decided on a washer with an actual radius in the range of 3.9 ≤ C ≤ 4.1.

Inequality is defined as the connection of an equation having the symbol ( ≤, ≥, <, >) in place of the assignment operator.

Here,

C = 3.14d

Given inequality,

3.9 ≤ C ≤ 4.1

3.9 ≤ 3.14d ≤ 4.1

dividing both sides of the inequality by 3.14,

1.242 ≤ d ≤ 1.305

As a result, the needed matching spacing for the washer's diameter is 1.242 ≤ d ≤ 1.305.

Learn more about intervals at

https://brainly.com/question/28382224?referrer=searchResults

#SPJ9

If the mean is 7171 grams, the standard deviation is 18 grams and 12 fruits are selected at random. Then, the mean weight will be 734.901 grams greater.

Let X be the random variable of the fruit's weight.

We have, the mean and standard deviation as 717 grams and 18 grams respectively.

We want to find the specific gram value for which 16% of the fruits are heavier, i.e. the 84th percentile of X's normal distribution

Now, Solving for x:

P( X < x ) = Normal( 717, 18 ), Z = 0.84

So,

P( [X - 717] / 18 < [x - 717] / 18 ) = P( Z < [x - 717]/18 ) = 0.84, where Z is a standard normal random variable

Now,

Standard Normal CDF( [x - 717]/18 ) = 0.84

Then, from the standard normal table: [x - 717]/18 = Inverse Standard Normal CDF( 0.84 ) = 0.9945

Therefore,

[ x - 717 ] / 18 = 0.9945

Multiplying 18 on each side of the equation,

x - 717 = 0.9945 × 18

x - 717 = 17.901

Adding 717 on each side of the equation,

x - 717 + 717 = 17.901 + 717

x = 734.901

Learn more about standard deviation here:

brainly.com/question/475676

#SPJ4

Answer: gurl you think i know

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the repeating decimal cost ...

  [tex]\$3.\overline{23}[/tex]

written as a fraction and as a mixed number.

One can convert the repeating decimal to a fraction by multiplying it by a power of 10 equal to the number of repeating digits.

This cost number (C) has 2 repeating digits (23), so we want to multiply it by 10^2:

  [tex]100C=10^2\times3.23\overline{23}=323.\overline{23}[/tex]

Now, we can subtract the original cost to cancel the repeating decimal fraction:

  [tex]100C -C = 323.\overline{23}-3.\overline{23}=320[/tex]

Dividing by the coefficient of C, we have the fraction we want:

  [tex]C=\boxed{\dfrac{320}{99}}[/tex]

This is expressed as a mixed number by figuring the quotient and remainder.

  [tex]\dfrac{320}{99}=\boxed{3\dfrac{23}{99}}[/tex]

Answer:

11

Explanation:

if you want to find the answer to a question like this just put the square root symbol on to your calculator before you type the number it wants you to get an answer for and the correct answer will appear

hope this helps:)

Answer:

11

Step-by-step explanation:

[tex]\sqrt{121} = \sqrt{11^{2} } = 11[/tex]

Answer: undefined

Step-by-step explanation:

The option (A) x → -∞, f(x) → ∞ and x → ∞, f(x) → -∞ if the polynomial function is  f(x) = -x⁵ + 9x⁴ - 18x³.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The polynomial function is:

f(x) = -x⁵ + 9x⁴ - 18x³

After plotting the graph of the polynomial function:

From the graph;

x → -∞, f(x) → ∞

x → ∞, f(x) → -∞

Thus, the option (A) x → -∞, f(x) → ∞ and x → ∞, f(x) → -∞ if the polynomial function is  f(x) = -x⁵ + 9x⁴ - 18x³.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

Answer:

Tony will spend 15$.

Step-by-step explanation:

2.50 * 6= 15($)

The first quartile of the given data set would be 15 which is The middle of the numbers from the beginning up.

When data points are organized in ascending order, the first quartile, or lower quartile, (Q1), is the value at which 25% of them are located.

The given data set is:

11,12,15,16,17,19,22,24,29,33,38

Since the number of elements in the data set is 11. As a result, the data are divided into two equal parts by the sixth term. The median of the data is 19.

The middle of the numbers from the beginning up to and including the first middle value: 11,12,15,16,17.

The middle value is 15.

Therefore, the first quartile of this data set would be 15.

Learn more about the first quartile here:

brainly.com/question/9707857

#SPJ1

The hypothesis test is a Left-tailed test and the parameter being​ tested is known as a Population mean.

What is a null and alternative hypotheses?

A null hypothesis predicts no effect between variables while an  alternative hypothesis predict an effect or relationship between variables of the study.

What is the given hypothesis test?

In the question, the given hypothesis test includes "H0​: σ=110" and "H1​: σ<110"

Hence, based on the test above, the hypothesis test is a Left-tailed test and the parameter being​ tested is known as a Population mean.

learn  more about of hypotheses here

https://brainly.com/question/27999628

#SPJ4

Step-by-step explanation:

With the equation

y

=

|

−

x

+

3

|

−

4

, we know that the term inside the absolute value mark will never be less than zero, which means the smallest

y

can be is

y

=

−

4

. This value is achieved with

|

−

x

+

3

|

=

0

, putting

x

=

3

. So that is our first point,

(

3

,

−

4

)

.

We're dealing with

x

terms (versus

x

2

or

√

x

or any other form of

x

), so the graph coming off

(

3

,

−

4

)

will be lines. Since there the coefficient of the

x

term is 1, the slope of those lines will be 1 and

−

1

(with the x term inside the absolute value, we look at both

±

1

).

The standard graph for an absolute value graph is for it to be in the shape of a V. And so we can expect our graph to have points

(

4

,

−

3

)

and

(

2

,

−

3

)

- and we can plug in those values to prove it:

y

=

|

−

x

+

3

|

−

4

−

3

=

|

−

4

+

3

|

−

4

−

3

=

|

−

1

|

−

4

−

3

=

1

−

4

−

3

=

−

3

and

−

3

=

|

−

2

+

3

|

−

4

−

3

=

|

1

|

−

4

−

3

=

1

−

4

−

3

=

−

3

The graph itself will look like this:

graph{abs(-x+3)-4 [-10, 10, -5, 5]}

Answer:

Step-by-step explanation:Price per pound of strawberries is $-0.31635 and blueberries is $0.6836.

Explanation :

Given data ;

Weight of strawberries required for dessert = 212 lb

Weight of blueberries required for dessert = 112 lb

Total cost spent = $9.50

Let,

Cost of blueberries per pound =x

Cost of strawberries per pound = (x-1)

We know that,

Cost of blueberries for overall weight + Cost of strawberries for overall weight = Total cost spent on fruits.

x(112) + (x-1)212 = 9.50

112x + 212x – 212 = 9.50

324x = 221.5

X = 221.5/324

X = $0.6836

So, (x-1) = $-0.31635

To learn more about pound click here :

https://brainly.com/question/23268373

#1234

Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794

Given that ;

Ben is making a dessert that requires 212 lbs of strawberries and 112 lbs of blueberries. Strawberries cost $1 less per pound than blueberries. Ben spent a total of $9.50 on the fruit.

So according to the question get the price per pound of each type of fruit;

Let ' x ' be the price per pound of strawberries and ' y ' be the price per pound of blueberries.

By assuming the following equations;

212x - 112y = 1 → ( I )

212x + 112y = 9.5 → ( II )

By solving above equations ( I ) ( II ) we get;

424x = 10.5

      x = 10.5/424

      x = 0.02476

224y = 8.5

      y = 8.5/224

      y = 0.03794

Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794

To learn more about Pound click here:

brainly.com/question/27994061

#SPJ4

The answer to the question -|4-7|+3  is 0  .

The Absolute Value of x denoted by |x| is the non negative value of , without regarding its sign .

For example the absolute value of -3 will be |-3| = 3 .

and absolute value of |-2| = 2 .

In the question ,

it is given that

the question is -|4-7|+3 .

and we have to find the answer of -|4-7|+3 .

let the answer be "y"

So , y = -|4-7|+3

= -|-3| + 3

On further simplification ,

we get  ,

= -(3) + 3     because |-3| = 3

= -3 +3

= 0

Therefore , The answer to -|4-7|+3  is 0  .

Learn more about Simplification here

https://brainly.com/question/18077352

#SPJ1

The number of jumbo cans of frosting would she need to frost 280 cupcakes is 8.

Given that, Bette used 3 jumbo cans of frosting to frost 105 cupcakes and 5 jumbo cans of frosting to frost an additional 175 cupcakes.

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Let number of jumbo cans of frosting would she need to frost 280 cupcakes be x.

Now the proportion is

3/105 = 5/175 = x/280

⇒ 5/175 = x/280

⇒ 175x = 280 × 5

⇒ x = 1400/175

⇒ x = 8

Therefore, the number of jumbo cans of frosting would she need to frost 280 cupcakes is 8.

To learn more about the proportions visit:

https://brainly.com/question/7096655.

#SPJ1

Suppose that y varies directly with x and that y=84 when x=7. What is the value of x when y=108?

when y=84 and when x=7, x to y in proportion is 1:12. Keeping the ratio of x to y at 1 to 12, when y = 108, x = 9.

Answer:

If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number. If the numbers are arranged from the greatest to the least, then it is called descending order.

Absolute Value Calculator: Heron's Calculator

Coterminal Angle Calculator: Graphing Functi...

Step-by-step explanation:

64 fluid ounces contain 1920 milliliters.

Oz to Half Gallon Conversions

A half gallon is equal to 64 ounces in a gallon measurement.

A milliliter is equal to how many ounces. The conversion factor from fluid ounces to milliliter is 1 fluid ounce = 30 milliliter.

This equates to eight 8-ounce glasses or 2,000 ml (approximately 64 ounces) for a person who consumes 2,000 calories per day.

Given: She regularly drinks 64 fluid ounces of water.

       1 fluid = 30 milliliters

       => 30 × 64 = 1920 milliliters

To know more about 64 oz of liquid visit:-
https://brainly.com/question/439009

#SPJ13

Answer:

Total cost: C(x) = 90,000 + 200x in dollars

C(100) = $110,000

This means that the total cost for the company when it produces 100 bikes would be $110,000

Step-by-step explanation:

First, you have a fixed cost, so you would start by setting C(x) to that:

C(x) = 90,000

Then, you have a cost of $200 PER bike that is made. The amount of bikes is represented by x. So you will have to multiply cost per bike by how many bikes are manufactured:

200x

Add this variable cost to the function underlined above.

C(x) = 90,000 + 200x

This is your function C(x).

Now for C(100), PLUG IN 100 for x:

C(100) = 90,000 + 200(100)

Multiply out:

C(100) = 90,000 + 20000

Then add these together to get the value:

C(100) = 110,000

This is the amount of money it would cost to make 110000 bikes, as interpreted above.

The ordered pairs that represent points on the graph of the equation 3x + 2y = -12. is; point (-4,0)

An equation of the line is defined as the linear equation that has a degree of one. The equation of the line contains two variables x and y. Thus, the third parameter will be the slope of the line which represents the elevation of the line.

The general form of the equation of the line is y = mx + c

where;

m is the slope

c is the y-intercept

We will find the ordered pair that satisfies the equation with each pair of points as;

3(-6) + 2(7) = -4

3(-4) + 2(0) = -12 YES

3(0) + 2(7) = 14

3(3) + 3(-3) = 0

3(6) + 2(0) = 18

The only ordered pair that satisfies the given linear equation is (-4, 0)

Read more about ordered pairs at; https://brainly.com/question/1528681

#SPJ1

Complete question is;

Which ordered pairs represent points on the graph of this equation? Select all that apply.

3x + 2y = -12

(-6, 7)

(7, 6)

(-4,0)

(0,7)

(3,-3)

(6,0)

Answer: m(slope) = -3/4, b(y-int) = -7/4

Answer:

The slope is -3/4 and the y intercept is 74.

Step-by-step explanation:

I just know I had this question.

Answer:

10% of 25 is 5/2 or 2½ as a fraction and 2.5 as a decimal. Let's find 10% of 25.

Step-by-step explanation:

The polynomial can be reduced to -9x^4

To solve this, we can simply add the similar polynomials or polynomials with the same power. This will help us simplify the polynomial to the lowest possible value.

[tex]-7x^4 + 4x^4 -6x^4 = -9x^4[/tex]

The polynomial given is simplified to become -9x^4

Learn more on addition of polynomials here;

https://brainly.com/question/17517586

#SPJ1

The equation of the line that passes through (-2, 5) and (−2,−8) is: x = -2.

The equation of a line that passes two given points on the line, can be expressed in slope-intercept form as y = mx + b. In this form, the variable "m" represents the slope of the line, while the "b" represents the y-intercept.

Find the slope using the two points  (-2, 5) and (−2,−8):

Slope (m) = change in y / change in x = (-8 - 5)/(-2 -(-2))

Slope (m) = -13/0 [cannot divide]

The slope of the line is undefined. This means the line is a vertical line that intercepts the x-axis at -2.

The equation of the vertical line would therefore be: x = -2.

Learn more about equation of a line on:

https://brainly.com/question/13763238

#SPJ1